Welfare Implications of Capital Account Liberalization
Ester Faia∗
Universitat Pompeu Fabra
August 2006
Abstract
In recent decades, capital account liberalization in emerging economies has often been followed by a surge in capital inflows, despite the presence of severe informational asymmetries for
foreign lenders. Empirical studies have shown that in emerging economies financial liberalization has led to an increase in consumption volatility (also relative to output). I use a small open
economy model where foreign lending to households is constrained by an endogenous borrowing
limit. Borrowing is secured by collateral in the form of durable investment whose accumulation
is subject to adjustment costs. This economy is able to replicate the aforementioned stylized
fact in response to various shocks (productivity, foreign demand and government expenditure).
I find that financial liberalization reduces welfare since it increases the volatility of consumption
and employment.
JEL Codes: E52, F1.
Keywords: endogenous borrowing limit, financial liberalization, consumption volatility.
∗
I thank participants at XV International Tor Vergata conference in Banking and Finance. I gratefully acknowledge
financial support from the DSGE grant of the Spanish Ministry and Unicredit research grant. All errors are my own
responsibility. Correspondence to: Department of Economics, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27,
08005, Barcelona, Spain. Email: ester.faia@upf.edu. Homepage: http://www.econ.upf.edu/~faia.
1
1
Introduction
It is well documented that since the mid-1980s there has been a surge in capital flows toward
emerging economies and that several developing countries have undertaken reforms to remove capital controls1 . This occurred despite the fact that financial markets in emerging countries are not
yet well developed and that still severe informational asymmetries characterize foreign lending.
Empirical evidence also shows that, contrary to conventional wisdom, for emerging countries the
increase in capital flows has induced an increase in consumption volatility (even relative to that
of output). This is the opposite of what we observe for industrialized economies where financial
integration is typically associated with an increase in consumption smoothing possibilities. Since
consumption volatility has a direct impact on agents’ utility we should conjecture that financial
liberalization produced welfare detrimental effects in emerging market economies.
To account for the aforementioned stylized facts and to evaluate the welfare effects of capital
account liberalization I use a small open economy model where risk averse agents finance consumption and investment in durable goods with foreign lending which is constrained by an endogenous
borrowing limit. Accumulable durable investment plays the role of collateral and can be seized by
foreign lenders in the event of default. The main assumptions embedded in the model respond to
the need of reproducing the conditions characterizing emerging market economies. Those countries
are small open economies which are characterized by frictions in the financial markets and have
undergone a wave of financial liberalization. The latter dimension is captured in the present model
by the parameter characterizing the sensitivity of foreign lending to the value of collateral (a higher
value of this parameter relaxes the limit to foreign borrowing).
I study the quantitative properties of this model economy in response to a variety of shocks:
productivity, government expenditure and foreign demand shocks. Productivity and government
expenditure shocks are introduced since they are typically considered as a main source of business
cycle fluctuations. Foreign demand shocks are regarded in the literature as an important source
1
See Lane and Milesi-Ferretti (2001), Obstfeld and Taylor (2002), Prasad, Rogoff, Wei and Kose (2005), among
others.
2
of business cycle fluctuations mostly for emerging market economies2 . Government expenditure
shocks play the role of demand shocks.
Consistently with empirical evidence I find that an increase in financial liberalization increases
consumption volatility in response to shocks even relative to that of output. This is so since an
increase in the sensitivity of foreign lending to the value of collateral has a twofold effect. Consider
a shocks which boosts the economy and increases demand. First, a higher degree of financial
liberalization, by relaxing the borrowing limit, induces a positive wealth effect. Indeed higher
availability of foreign lending allows for a bigger increase in the demand for both durable and nondurable goods. Secondly, when an additional unit of collateral becomes available the shadow value
of relaxing the liability constraint is higher the bigger the sensitivity of foreign lending to collateral.
This is a distortion effect which tends to decrease the current value of durable goods relative to
that of non-durable goods and induces agents to substitute durable investment with consumption.
I finally consider the welfare consequences of financial liberalization and find that it is welfare
detrimental in an economy with imperfect risk sharing3 . This is so since financial liberalization
increases both consumption and employment volatility thereby reducing the welfare of risk averse
agents. A crucial feature of the welfare analysis is the use of second order approximated solutions
which allow
4
to account for the effects of stochastic volatility both on first and second moments
of the variables that enter agents’ utility.
The rest of the paper is divided as follows. Section 2 presents related literature and empirical
evidence. Section 3 presents the model and calibration. Section 4 presents the results. Section 5
concludes.
2
See Mendoza (1995) and Senhadji (1998).
It is assumed that the borrowing constraint is always binding for any level of financial liberalization. In other
words, welfare decreases with respect to an increase in financial liberalization under the assumption that the financial
markets are credit constrained. Obviously welfare would increase if the economy was to move from a steady state
with binding credit constraints to one with non-binding ones. I do not consider this long run growth effect since it
would not apply to developing countries.
4
See Kim and Kim (2003) for an analysis of the inaccuracy of welfare calculations based on log-linear approximations in dynamic open economies.
3
3
2
Empirical Evidence and Related Literature
It is well documented that in the last two decades emerging market economies have undertaken
reforms that favoured financial integration and that there has been an increase in capital flows
toward those countries (see Lane and Milesi-Ferretti (2001), Obstfeld and Taylor (2002), Prasad,
Rogoff, Wei and Kose (2005), among others). This wave of financial integration occurred despite
the fact that financial structures in emerging economies are still not yet well developed.
Conventional wisdom suggests that financial integration increases consumption smoothing and
reduces macroeconomic volatility through an increase in risk sharing possibilities. To this purpose
several empirical studies have analyzed the impact of an increase in capital flows on macroeconomic
volatility for emerging market economies. Contrary to what expected Gavin and Hausmann (1996)
and O’Donnell (2001) find a positive link between capital flows and output volatility for emerging
market economies. They argue that financial integration increases risk sharing possibility (hence
reduces macroeconomic volatility) only in countries with well developed financial markets, while it
increases vulnerability to foreign shocks in the opposite case.
Bekaert, Harvey and Lundblad (2002), Kose, Prasad and Terrones (2003) and Prasad, Rogoff,
Wei and Kose (2005) find that in emerging market economies an increase in financial openness tends
to increase consumption volatility (even relative to that of output). They also point out at the
limited role of international risk sharing for economies whose financial markets are characterized
by higher degrees of informational asymmetries and poor financial development.
While several empirical studies agree on the positive link between financial openness and
macroeconomic volatility, a large part of the theoretical literature fails to account for aforementioned observation. Most of the theoretical contributions focusing on the relation between financial
integration and macroeconomic volatility have analyzed the case of industrialized countries and
concluded that financial openness tends to decrease consumption volatility (see Mendoza (1994)
and Baxter and Crucini (1995)) since it increases risk sharing possibilities. Some theoretical studies
have shown that the impact of financial openness on macroeconomic volatility depends the source
of shocks, fiscal versus monetary shocks (see Obstfeld and Rogoff (1995), Sutherland (1996)), while
4
others (Heatcote and Perri (2005) and Faia (2003)) have shown that financial openness tends to
decrease international co-movements in business cycles.
More recently Levchenko (2005) uses a framework with limited commitment as in Kocherlacota
(1996) and shows that domestic risk sharing arrangements might deteriorate in face of financial
integration. He finds that in this case individual consumption might become more volatile but
aggregate consumption volatility will nevertheless decrease, a result which is still in contrast with
empirical predictions.
In the present paper we propose a simple framework which combines financial frictions and
capital account liberalization and tries to reconcile empirical evidence with theoretical predictions.
3
A Small Open Economy with Endogenous Borrowing Limits on
Durable Goods Investment
The model economy features several similarities with the one considered in Kocherlacota (2000) and
Chari, Kehoe and McGrattan (2005). It is a small open economy where agents’ consumption and
investment is subject to endogenous borrowing limit a’ la Kiyotaki and Moore (1998). There are
three main differences with the aforementioned studies. First, collateralizable wealth is represented
by durable goods which also provide utility services (see Mankiw (1987), Miles (1992) and Iacoviello
(2004)) and can be accumulated with adjustment costs. This assumption allows to reproduce
persistence in response to various shocks (see Erceg and Levin (2004)). Secondly, agents supply
labor endogenously. This assumption allows for a better characterization of the welfare effects of
macroeconomic volatility. Third, I consider a small open economy which produces and trades with
the rest of the world imperfectly substitutable goods. The last assumption allows for a better
characterization of the current account dynamic.
The economy is populated by infinitely lived and risk averse agents who consume, work and
invest in durable goods. Consumption and durable investment is financed through foreign lending
which takes the form of non—state contingent securities and is bounded above by a fraction of the
future value of the collateral - i.e. durable goods. Hence the capital flow dynamic of the small open
economy is directly linked to the tightness of the borrowing limit. Investment demand for durable
5
is justified since it enters the utility functions of the consumers. The assumption of a financially
constrained small open economy is justified by the inability of foreign lenders to implement perfect
monitoring of the investment activity. Under those circumstances the tightness of the borrowing
limit depends on the degree of information asymmetry, of financial market integration and of
debt repossession ability which in turn depends upon legal and institutional arrangements. The
production sector of this economy is characterized by final good firms who produce with a linear
production technology using labor.
3.1
Domestic Households
Let st = {s0 , ....st } denote the history of events up to date t, where st denotes the event realization
at date t. The date 0 probability of observing history st is given by ρt . The initial state s0
is given so that ρ(s0 ) = 1. Henceforth, and for the sake of simplifying the notation, let’s define
P
the operator Et {.} ≡ st+1 ρ(st+1 |st ) as the mathematical expectations over all possible states of
nature conditional on history st .
Agents maximize the following expected discounted sum of utilities:
Et
(∞
X
t=0
t
β U (Ct ) − V
)
∼
(Nt ) + ∆(Dt )
(1)
where Nt denotes total labour hours, consumption:
µ
¶ η
η−1
η−1
η−1
1
1
η
η
η
η
Ct = (1 − α) CH,t + α CF,t
(2)
is given by a Dixit-Stiglitz consumption aggregator of domestic and imported goods (with η being
∼
the intratemporal elasticity) and Dt = Dt −
ψ Xt −δDt 2
)
2 ( Dt
where Dt is the real value of the stock
of a durable good which is hold in positive amount for it generates utility, Xt is investment in
durable goods, δ is the depreciation rate and the function
ψ Xt −δDt 2
)
2 ( Dt
represents an adjustment
cost function. The period utility function is separable in each of its argument. After defining
1
1−η
1−η 1−η
Pt ≡ [(1 − γ)PH,t
+ γPF,t
]
as the domestic price index and st =
PF,t
PH,t
as the terms of trade,
optimal demands for domestic and imported goods imply the following relation:
CH,t
(1 − α)
(st )η
=
CF,t
α
6
(3)
The household receives at the beginning of time t a labor income of Wt Nt , where Wt is the
nominal wage. Agents can borrow and lend in the world market at an interest rate R (which is
assumed time invariant for simplicity). I denote by Bt the real amount (denominated in units of
domestic consumption) of the net foreign asset position. Agents can also buy and sell durables, Dt ,
in an internal competitive market. The price of durable in terms of consumption goods is denoted
Zt .
The sequence of budget constraints in real terms reads as follows:
Ct + RBt + Zt (Dt+1 − Dt (1 − δ)) ≤
Wt
Nt + Bt+1 + τ t
Pt
(4)
The crucial assumption in this model is that agents face borrowing constraints on the world
market. As the foreign lenders are not able to fully repossess their funding, debt and its services
are guaranteed as repayable up to a certain fraction of the value of the collateral (limited liability
constraint). The collateral corresponds to the future value of the durable good Zt+1 Dt , where Z is
the price of the durable good. To formalize this idea I assume that domestic households face the
following period-by-period endogenous borrowing constraint on debt:
RBt+1 ≤ Ω Et {Zt+1 Dt+1 }
(5)
where:
Ω<1
is the fraction of the future value of the collateral that is guaranteed to be repaid. Hence Ω reflects
the degree of information asymmetry, of financial market integration and of debt repossession
ability of foreign lenders which in turn depends upon legal and institutional arrangements. Since
increasing Ω allows to relax the borrowing limit and to increase the availability of foreign lending,
I will assume that higher degree of financial liberalization is associated with higher value of Ω.
Notice that domestic households face limited liability but not a risk of defaulting on the debt. This
implies that the borrowing constraint always holds with equality. To ensure this it is enough to
assume that β < R−1 .
7
Households choose the set of processes {Ct , Nt , Bt+1 , Dt+1 }∞
t=0 taking as given the set of
processes {Pt , Wt , R, Zt }∞
t=0 and the initial wealth B0 , D0 so as to maximize (1) subject to (4)
and (5). Let’s define λt as the Lagrange multipliers on constraint (5). The following optimality
conditions must hold:
Uc,t
Wt
= −Vn,t
Pt
(6)
Uc,t − λt = βEt {RUc,t+1 }
(7)
Dt+1 − Dt
Zt Uc,t − Zt+1 Ωλt + ∆ ∼ ψ(
)
(8)
Dt+1
Dt
¾
½
Dt+2 − Dt+1
ψ (Dt+2 − Dt+1 )2
)+
) + β(1 − δ) Et {Zt+1 Uc,t+1 }
= Et β∆ ∼ (1 + ψ(
2
Dt+1
Dt+1
2
Dt+1
∆
Zt =
∼
Dt+1
Uc,t
ψ(
Dt+1 − Dt
)
Dt
(9)
Equation (6) gives the optimal choice of labor supply. Equation (7) gives the price of the
foreign asset. Equation (8) is the efficiency condition for the intertemporal choice of the durable
good. The intuition for this equation is simple. The time t marginal cost of foregoing a unit of
consumption (weighted by the price of the durable) is equated to its marginal gain which has three
components. The direct marginal utility of an additional unit of durable investment now and in the
½
¾
−Dt+1
ψ (Dt+2 −Dt+1 )2
future, Et β∆ ∼ (1 + ψ( Dt+2
)
+
, the expected marginal utility of one unit
Dt+1
2
D2
Dt+1
t+1
of consumption postponed into the future, β(1 − δ) Et {Zt+1 Uc,t+1 } , and, for an additional unit of
collateral has become available, the shadow value of relaxing the liability constraint, Zt+1 Ωλt . The
last equation, (9), gives the asset price.
A few comments are worth on the distortions induced by the endogenous borrowing limit and
on the effects of varying Ω. First, as it stands clear from equation (7) a binding borrowing constraint (which implies a positive λt ) induces a intratemporal distortion in the value of consumption
between two different dates. By defining Rtc =
Uc,t
Et {Uc,t+1 }
8
as the households’ intratemporal price of
consumption, when (5) binds, households face the following endogenous finance premium5 :
Et {Rtc − R} =
λt
Et {Uc,t+1 }
(10)
This implies that it is now more costly and that a higher premium is required to perform a
shift in consumption between two different dates. An increase in the parameter Ω, by relaxing
the borrowing limit, reduces the responsiveness of the lagrange multiplier, λt ,to exogenous shocks,
therefore reducing the size of the finance premium.
Secondly, as it stands clear from equation (8) a binding borrowing constraint induces an
intertemporal distortion of size Zt+1 Ωλt in the value of durable consumption between two different
dates. An increase in the paramter Ω has both a direct and an indirect impact on the distortion.
The direct impact comes form the fact that the size of the distortion itself depends in Ω.The indirect
impact comes from the fact a higher value of Ω, by relaxing the borrowing limit, reduces the size
of λt , which enters the distortion as well. Even in this case the distortion has an impact on the
finance premium of durable investment and in turn on the volatility of the durable price.
3.2
Domestic Firms
There is a continuum of competitive firms in the domestic economy each producing an homogenous
final good. Each firm produces according to the following production function:
Yt = At Nt
(11)
The cost minimizing choice of labor input implies:
Wt
= At
Pt
3.3
(12)
Open Economy Relations
∗ = P ∗ .Furthermore I assume that the law
Under the small open economy assumptions we set PF,t
t
∗ = e P ∗ and P ∗ = e P ∗ where e is the nominal
of one pice holds continuously so that PH,t
t H,t
t F,t
t
F,t
5
The present model with endogenous borrowing limit is akin to models with endogenous financing premia such as
Carlstrom and Fuerst (1997) and Bernanke, Gertler and Gilchrist (1998) .
9
exchange rate. Foreign demand of home produced goods is modelled as follows:
∗
=(
CH,t
∗
PH,t
Pt∗
)η Ct∗
(13)
Applying the law of one price and substituting the definition of terms of trade we obtain:
∗
CH,t
= (st )η Ct∗
(14)
and where Ct∗ = Yt∗ . Foreign output is taken as exogenous by domestic residents and takes the
following autoregressive process:
∗ ρ
) + εYt
Yt∗ = (Yt−1
3.4
∗
Equilibrium Conditions
Aggregate bonds are in negative net supply and must satisfy the following conditions:
Rt+1 Bt+1 + ΩEt {Zt+1 Dt+1 } = 0
(15)
By substituting the real wage in the budget constraint of the domestic household using firms’
optimality conditions we obtain an equation that links net debt accumulation to net exports as
follows:
Rt+1 Bt+1 − Bt = Yt − (Ct + Zt Xt ) ≡ N Xt
(16)
Xt = Dt − Dt−1 (1 − δ)
(17)
where:
denotes investment in durable goods.
Equation (16) describes the current account dynamic which in this economy is governed by
the accumulation of foreign debt.
The resource constraint in this economy reads as follows:
∗
+ Xt + Gt
Yt = CH,t + CH,t
10
(18)
3.5
Calibration
Preferences. Time is measured in quarters. To ensure that the borrowing constraint is always
biding I assume that β < Rt−1 , therefore I set β = 0.966 . Utility is modeled as follows:
∼ 1−γ
D
N 1+τ
Ct1−σ
− t
+ t
1−σ
1+τ
1−γ
The parameter σ is set equal to 2 as in Schmitt-Grohe and Uribe (2003) and in most models of
small open economies for emerging markets. The parameter τ is set equal to 3 since it is assumed
that 1/3 of the time is spent working. The parameter γ is set equal to 2 implying that preferences
over durables exhibit a somewhat lower intertemporal substitution elasticity than the logarithmic
case; this value falls within the range estimated by the empirical literature.
Technology. Consistently with Erceg and Levin (2002) I set ψ = 600. The quarterly depreciation rate of the durable stock is set to δ = 0.025; this value is consistent with a specification
of the durable investment which includes both consumer durables and residential investment. I
set the baseline parameter that defines the tightness of the endogenous borrowing limit so as to
induce a steady state debt to equity (leverage) ratio of 0.4. Following Backus, Kehoe and Kydland
(1995) the elasticity of substitution between home and foreign consumption, η, is set to 1.5. Finally
the share of home consumption good, α, is chosen such that the steady state sum of exports and
imports is 40 percent of output.
Stochastic processes. Following Prescott (1986) and McCallum and Nelson (1999) the standard
deviation of the productivity shock is set to 0.007 and its persistence is set to 0.957 . To determine
6
We focus on the case in which the collateral constraint binds since the dynamic of the model in the opposite case
would look exactly as the one that characterize a standard RBC model with endogenous labor supply and trade in
imperfectly substitutable goods.
7
There is little consensus about the statistical properties of the productivity shock in emerging market economies.
For example Senhadji (1997), Mendoza and Smith (2006) and Mendoza (2006) choose (different) values for the
variance and the persistence of TFP which allow to reproduce GDP volatility for various emerging market economies.
Aguiar and Gopinath (2005) show that for emerging market economies a productivity process that allows to fit the
data should contain both a permanent and a transitory component, a conclusion contested by Garcia-Cicco, Pancrazi
and Uribe (2006). Kydland and Zarazaga (2003) show that a TFP process with a persistence of ρ = 0.56 and a
1
standard deviation of (1−ρ)
2 can fit well Argentinian business cycle. Given the lack of consensus I have chosen a
standard RBC parametrization for the productivity process. This is a conservative parametrization which allows
to appreciate better the contribution of the borrowing constraint to the model dynamic. It is important to notice
however that I have performed several sensitivity analysis on the shock processes and the that the main quantitative
results remained unaffected.
11
the statistical properties of the foreign demand shock I measure world output as U.S. real GDP and
using OECD quarterly data for the period 1970-2001 I seek for innovations by fitting an autoregressive process with time trend. I find that σ εY ∗ = 0.00885. The share of government expenditure over
t
GDP in the steady state is set equal to 0.2. Finally the calibration of the government expenditure
shock follows Carmichael, Keita and Samson (1999) who estimate for emerging market economies
a process with a persistence of 0.46 and a standard deviation of 0.14 percent.
The set of optimality conditions of the optimal plan can be described as follows:
Et { H(Ψt+1 , Ψt , Xt+1 , Xt )} = 0
(19)
where Et denotes the mathematical expectations operator, conditional on information available at
time t, Ψt is the vector of endogenous non-predetermined variables, and Xt ≡ [x1,t , x2,t ] is the state
vector. The solution of the model is of the form (Schmitt-Grohe and Uribe (2004)) :
Ψt = g(Xt , ξ)
(20)
−
(21)
Xt+1 = h(Xt , ξ) + ηξ εt+1
Equation (20) and (21) describe the policy function and the transition function respectively. I
compute a second order expansion of the functions g(Xt , ξ) and h(Xt , ξ) around the deterministic
steady-state.
4
Quantitative Properties of the Model
We now turn to the analysis of the quantitative properties of the model with two purposes in mind.
First, I aim to show that the model is compatible with the main stylized facts exposed in section
2. Secondly, I use the model to evaluate the welfare effects of increasing financial liberalization.
4.1
Dynamic Responses to Shocks
Before analyzing the business cycle properties of the model it is instructive to illustrate the dynamic
responses of selected variables to various shocks. Figure (1) shows impulse responses of selected
12
variables to a 1% increase in productivity. An increase in aggregate productivity increases output
and wage wealth which in turn induces an increase in consumption of both, durable and non-durable
goods. The increase in the demand of durable goods induces an increase in the price of durable
which in turn raises the future value of collateral. Finally, the increase in the value of collateral
relaxes the borrowing limit therefore increasing the availability of loans and further raising the
demand for durable and non-durable goods. As a consequence of the increase in the availability of
foreign lending the current account becomes negative and terms of trade depreciate. It is worth
noticing that all variables show hump-shaped dynamics; this is due to the persistence introduced
by the cost of adjusting durable investment.
Figure (2) shows impulse responses of selected variables to a positive foreign demand shock. An
increase in foreign demand renders positive the current account therefore inducing appreciation of
the terms of trade. The positive dynamic of the current account induces an outflow of capital which
reduces the availability of foreign lending, the demand of durable goods and its price. Aggregate
consumption of non-durable goods increases temporarily due to the positive boosts coming from
the increase in the consumption of home produced goods, but it decreases after a few periods due
to the fall in the availability of lending.
Figure (3) shows impulse responses of selected variables to a government expenditure shock.
An increase in government expenditure crowds out the demand for durable and non-durable consumption. The price of the durables falls and consequently the value of collateral decreases. This
tightens the borrowing limit and reduces the availability of foreign lending.
4.2
Consumption Volatility and Financial Openness
Figure (4) shows changes in the volatility of consumption with respect to changes in the tightness of
foreign lending described by the parameter Ω. The model has been solved under both productivity
and foreign demand shocks, as they are considered the main source of fluctuations in emerging
market economies. I find that consumption volatility is monotonically increasing with respect to
the degree of financial openness. This is so since an increase in the parameter Ω has a twofold
effect. First, there is a wealth effect due to which an increase in Ω makes the borrowing limit
13
less tight therefore increasing the availability of foreign lending for every size of the shock. The
increase in the availability of foreign lending allows for a bigger increase in the demand for both
durable and non-durable goods. Secondly, as it stands clear from equation (8) when an additional
unit of collateral becomes available the shadow value of relaxing the liability constraint, Zt+1 Ωλt
is higher the bigger is the size of Ω. This is a distortion effect which tends to decrease the current
value of durable goods relative to that of non-durable goods and induces agents to substitute
durable investment with consumption. We observe indeed that while the sensitivity of non-durable
consumption in response to shocks increases when Ω increases, the contrary is true for the demand
in durable goods.
To check robustness I also study the effects of trade openness (as measured by the ratio of
exports over GDP α) on consumption volatility and find little effect8 , a result consistent with
empirical evidence (see Easterly, Islam and Stiglitz (2001) and Kose, Prasad and Terrones (2003)).
Furthermore, I find that consumption volatility relative to output volatility also increases with
respect to Ω. Indeed relative consumption volatility goes from 0.9049 to 0.9962 when Ω goes from
0.2 to 0.8. This result is consistent with Bekaert, Harvey and Lundblad (2002), Kose, Prasad and
Terrones (2003) and Prasad, Rogoff, Wei and Kose (2005) who point out that the increase in
consumption volatility cannot be associated with crises episodes since we also observe an increase
in relative (to output) consumption volatility.
4.3
Welfare Implications
The critical feature of the analysis so far conducted consists in evaluating the impact of capital
flow liberalization on household’s welfare. We have shown previously that an increase in financial
openness induces an increase in macroeconomic volatility, hence we are now interested in assessing
its impact on welfare. To fully account for the effects of the increased volatility on welfare I solved
the model using second order approximations9 which allow to account for the effects of stochastic
8
Results are not reported for brevity but are available upon request.
See Kim and Kim (2003) for an analysis of the inaccuracy of welfare calculations based on log-linear approximations in dynamic open economies. See Kim et al. (2003) and Schmitt-Grohe and Uribe (2004a) for a more general
discussion.
9
14
volatility both on first and second moments of the variables in the model10 .
The welfare metric employed is given by the conditional expectation of the second order Taylor
expansion of agents’ utility:
W0 =
(
E0
∞
X
∼
)
β t U (Ct , Nt , Dt )
t=0
(22)
Figure (5) shows changes in welfare with respect to changes in the parameter Ω ranging from
0.4 to 0.8. Agents’ welfare is clearly decreasing with respect to the parameter defining the degree
of financial liberalization. The reason for this is simple. A raise in in the parameter Ω increases
both the volatility of consumption and employment. Since agents are risk averse the increase in
volatility reduces welfare. Notice that this occur despite the fact that the volatility of durable
goods is decreasing with respect to the same parameter.
Before closing it is worth exploring whether the negative link between welfare and financial
openness remains unchanged for different values of the elasticity of demand for durables. This
parameter indeed affects the volatility of durable goods. More specifically the higher is the value
of γ the lower is the volatility of durable goods in response to shocks. Figure (6) shows changes
in welfare with respect to changes in the parameter that defines financial openness, Ω, and for
two different values of γ (1.5 in the top panel graph and 3 in the bottom panel graph). Financial
openness remains welfare detrimental for every value of the elasticity for durable goods. Additionally
we observe that higher values of γ by reducing the volatility of durables tend to raise welfare.
10
Since in a first order approximation of the model’s solution the expected value of a variable coincides with its
non-stochastic steady state, the effects of volatility on the variables’ mean values is by construction neglected. Hence
we can fully appreciate the effects of volatility on welfare only by resorting to a higher order approximation of the
policy functions.
15
References
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Cycles”. Journal of Political Economy, 101, 745-775.
[3] Baxter, Marianne and Mario Crucini. (1995) “Business cycles and the Asset Structure of
Foreign Trade”. International Economic Review, 36, 821-54.
[4] Bekaert, G., C.R. Harvey, and C. Lundblad. (2002) “Growth Volatility and Equity Market
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19
CONSUMPTION
DURABLES STOCK AND INVESTMENT
0.6
0.4
0.4
0.3
0.2
0.2
0
0.1
−0.2
0
10
20
30
40
50
60
0
0
10
20
PRICE OF COLLATERAL
0.08
0.2
0.06
0.1
0.04
0
0.02
0
10
20
30
40
40
50
60
40
50
60
50
60
DEBT
0.3
−0.1
30
50
60
0
0
10
TERMS OF TRADE
20
30
DOMESTIC AND FOREIGN DEMAND
0.6
0.4
0.2
0.4
0
0.2
−0.2
0
−0.2
−0.4
0
10
20
30
40
50
60
−0.6
0
10
20
Figure 1: Impulse responses to domestic productivity shocks.
20
30
40
−14
2
−14
CONSUMPTION
x 10
5
DURABLES STOCK AND INVESTMENT
x 10
4
0
3
−2
2
−4
−6
1
0
10
−14
3
20
30
40
50
60
0
10
20
−15
PRICE OF COLLATERAL
x 10
0
4
30
40
50
60
40
50
60
50
60
DEBT
x 10
2
2
1
0
0
−1
0
10
20
30
40
50
60
−2
0
10
TERMS OF TRADE
0.6
−0.1
0.4
−0.2
0.2
−0.3
0
−0.4
−0.2
0
10
20
30
30
DOMESTIC AND FOREIGN DEMAND
0
−0.5
20
40
50
60
−0.4
0
10
20
Figure 2: Impulse responses to foreign demand shocks.
21
30
40
CONSUMPTION
DURABLES STOCK AND INVESTMENT
0.05
0
−0.02
0
−0.04
−0.05
−0.06
−0.1
−0.15
−0.08
0
10
20
30
40
50
60
−0.1
0
10
20
PRICE OF COLLATERAL
0
0.05
−0.005
0
−0.01
−0.05
−0.015
0
10
20
30
40
40
50
60
40
50
60
50
60
DEBT
0.1
−0.1
30
50
60
−0.02
0
10
TERMS OF TRADE
20
30
DOMESTIC AND FOREIGN DEMAND
0.05
0.15
0.1
0
0.05
−0.05
0
−0.1
−0.15
−0.05
0
10
20
30
40
50
60
−0.1
0
10
20
30
Figure 3: Impulse responses to government expenditure shocks.
22
40
Consumption volatility: effect of varying tightness of borrowing constraint
Consumption volatility (in percentage deviations)
1.4
1.35
1.3
1.25
1.2
1.15
1.1
1.05
1
0.95
0.9
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Tightness of borrowing constraint
Figure 4:
23
0.9
1
Changes in welfare with respect to changes in OMEGA
32
30
28
26
24
22
20
18
0.4
0.45
0.5
0.55
0.6
Figure 5:
24
0.65
0.7
0.75
0.8
GAM=1.5
32
30
28
26
24
22
20
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.65
0.7
0.75
0.8
GAM=3.5
34
32
30
28
26
24
22
20
18
0.4
0.45
0.5
0.55
0.6
Figure 6: Changes in welfare with respect to changes in financial openness for two different values
of γ.
25